PASSIVE COMPONENTS Understanding the distortion mechanism of high-K MLCCs By John Caldwell The underlying mechanism causing distortion when using High-K ceramic capacitors in a system’s signal path is the voltage coefficient of capacitance (VCC) of the capacitor. The term VCC is used to describe the change in the value of a capacitor with respect to the magnitude of the applied voltage. Power supply designers are well aware of this behaviour as it can directly affect the output ripple or stability of their system, but VCC is often ignored in small-signal circuitry. In order to understand why the capacitance varies with applied voltage and how the VCC varies with other capacitor parameters, Fig. 2: An example of the dependence of barium titanate’s relative permittivity on the intensity of the applied electric field. it is necessary to first look at a capacitor’s basic structure. Fig. 1: A basic parallel plate capacitor with electrode plates of area A and a separation distance d. Figure 1 shows a simple capacitor consisting of two plate electrodes of area A, separated a distance d by a dielectric (green). The capacitance of this structure is given by equation 1: where εo and εr are the permittivity of free space and relative permittivity of the dielectric, respectively. The magnitude of the electric field applied to the dielectric is a function of the applied voltage and the separation distance between the two plates. The voltage coefficient of many capacitors arises from the electrostatic force on the dielectric when a voltage is applied to the capacitor. Because the dielectric material cannot be infinitely stiff, it is compressed by this force, reducing the separation distance d and increasing the capacitance. Multilayer ceramic capacitors, on the other hand, exhibit an additional negative voltage coefficient that arises from other properties of the dielectric. Ceramic capacitors owe their small size, high capacitance, and low cost to the use of barium titanate in the dielectric, which provides an extremely high relative permittivity. Unfortunately, this material’s relative permittivity varies depending upon the intensity of the applied electric field – see figure 2. As the applied electric field is increased, the relative permittivity of the barium titanate is reduced, showing a 55% reduction over the tested range. Therefore, increasing the voltage applied to a ceramic capacitor reduces the relative permittivity of the barium titanate in the dielectric material, causing a decrease in capacitance. The electric field intensities in figure 2 may seem unlikely to occur in small signal circuits. However, in the pursuit of higher volumetric efficiencies, capacitor manufacturers are able to produce ceramic capacitors with dielectric thicknesses below 5 microns, creating surprisingly high electric field intensities. Using equation 2, we can see that applying 1V to a capacitor with a 5 μm dielectric thickness results in an electric field intensity of 200,000 V/m! Understanding this property of barium titanate allows us to infer some rules for the voltage coefficient of ceramic capacitors. First, the voltage coefficient is worst (greatest change with applied voltage) in ceramic capacitors with the highest barium titanate content. Table 1 displays the barium titanate content of selected ceramic dielectric types. Second, the voltage coefficient gets worse for smaller packages because the change in the relative permittivity is dependent upon the intensity of the applied electric field. As the capacitor’s package size is decreased, the area of the electrode plates is reduced. Therefore, the thickness of the dielectric must be reduced to maintain a certain capacitance. Voltage coefficient effects Although we’ve identified the mechanism for voltage coefficient of capacitance, it may not be immediately clear how this voltage coefficient causes distortion. Consider that because the value of a ceramic capacitor is, in reality, a function of the applied voltage, the equation for current through that capacitor must be modified. As shown in the equation below, the constant C for capacitance is replaced with a function C, which depends on the applied voltage V. We can extract the function C(V) from typical voltage coef- John Caldwell is an analog applications engineer for TI’s Precision Analog Linear Applications group – www.ti.com - John can be reached at ti_johncaldwell@list.ti.com 34 Electronic Engineering Times Europe January 2014 www.electronics-eetimes.com

EETE JAN 2014

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